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Question

We can calculate the volume V  of a rectangular prism using V=LWH, where L is the length, W is the width, and H  is the height of the prism. Suppose that a prism has a volume of 200 cm3 and L=2W.



a. Rewrite the volume formula by making substitutions for V  and L .

b. Rewrite the equation as h in terms of w(Turn it into h=something)

Answer 1

1 V_{rectangular prism} = L·W·H

2

3 SUPPOSE:

4 V = 200 cm³

5 L = 2W

6

7 a) rewrite the volume formula by making substitutions for V and L

8 V = L·W·H

9 ( ) = ( )·W·H

10

11 make the substitution

12 200 cm³ = (2W)·W·H ← see lines 4 and 5

13

14 simplify

15 200 cm³ = 2W²H

16

17 b) rewrite the equation as H in terms of W... write H(W) or height as a function of width

18 use algebra to solve the volume formula for H (instead of V)

19

20 NOTE: at this point, V has already been substituted for 200 cm³

21

22 H = 200 cm³

2W²